Outer common tangents and nesting of convex hulls in linear time and constant workspace

TY - GEN

T1 - Outer common tangents and nesting of convex hulls in linear time and constant workspace

AU - Abrahamsen, Mikkel

AU - Walczak, Bartosz

N1 - Conference code: 24

PY - 2016/8/1

Y1 - 2016/8/1

N2 - We describe the first algorithm to compute the outer common tangents of two disjoint simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies on the same side of the line. An outer common tangent of two polygons is a tangent of both polygons such that the polygons lie on the same side of the tangent. Each polygon is given as a read-only array of its corners in cyclic order. The algorithm detects if an outer common tangent does not exist, which is the case if and only if the convex hull of one of the polygons is contained in the convex hull of the other. Otherwise, two corners defining an outer common tangent are returned.

AB - We describe the first algorithm to compute the outer common tangents of two disjoint simple polygons using linear time and only constant workspace. A tangent of a polygon is a line touching the polygon such that all of the polygon lies on the same side of the line. An outer common tangent of two polygons is a tangent of both polygons such that the polygons lie on the same side of the tangent. Each polygon is given as a read-only array of its corners in cyclic order. The algorithm detects if an outer common tangent does not exist, which is the case if and only if the convex hull of one of the polygons is contained in the convex hull of the other. Otherwise, two corners defining an outer common tangent are returned.

U2 - 10.4230/LIPIcs.ESA.2016.4

DO - 10.4230/LIPIcs.ESA.2016.4

M3 - Article in proceedings

T3 - Leibniz International Proceedings in Informatics

BT - 24th Annual European Symposium on Algorithms (ESA 2016)

A2 - Sankowski, Piotr

A2 - Zaroliagis, Christos

PB - Schloss Dagstuhl - Leibniz-Zentrum für Informatik

T2 - 24th Annual European Symposium on Algorithms

Y2 - 22 August 2016 through 26 August 2016

ER -